It is known, that every graph is isomorphic to an induced subgraph of a categorical product of complete graphs [1]}. Consider a graph \(G\)  embedded into a categorical product of \(d\)  complete graphs \(K^1_{n_1}\times \dots \times K^d_{n_d}\) . Without loss of generality we may assume that \(n_1 = ... = n_d = n\) , i.e.
\(G\cong G^{\prime } \le S = (K_n)^d,\) 
